What is (\partial)/(\partial x)(4x^3y^3-3) ?

The answer to (\partial)/(\partial x)(4x^3y^3-3) is 12x^2y^3

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(\partial)/(\partial x)(4x^3y^3-3)

\frac{\partial}{\partial x} (4 x^{3} y^{3} - 3)

12 x^{2} y^{3}

Solution steps

\frac{\partial}{\partial x} (4 x^{3} y^{3} - 3)

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (4 x^{3} y^{3}) - \frac{\partial}{\partial x} (3)

\frac{\partial}{\partial x} (4 x^{3} y^{3}) = 12 y^{3} x^{2}

\frac{\partial}{\partial x} (3) = 0

= 12 y^{3} x^{2} - 0

Simplify

= 12 x^{2} y^{3}

y = \frac{e ^{- x}}{x + 1}, at x = 1

\frac{d}{d x} (\frac{2 x + 1}{x ^{2} - 1})

x^{2} - 1, - x + 2, x = 0 x = 1

x^{4} + 9 e^{x}

\frac{d y}{d x}, y = e^{x}

What is (\partial)/(\partial x)(4x^3y^3-3) ?
The answer to (\partial)/(\partial x)(4x^3y^3-3) is 12x^2y^3